What is the axis y=-x^2-3x+4 ?

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axis y=-x^2-3x+4

axis

y = - x^{2} - 3 x + 4

x = - \frac{3}{2}

Solution steps

y = - x^{2} - 3 x + 4

Rewrite

y = - x^{2} - 3 x + 4

in the standard form

4 (- \frac{1}{4}) (y - \frac{25}{4}) = (x - (- \frac{3}{2}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{3}{2}, \frac{25}{4}), p = - \frac{1}{4}

Parabola is of the form

4 p (y - k) = (x - h)^{2}

and is symmetric around the

y

-axis

Axis of symmetry is a line parallel to the

y

-axis which intersects the vertex:

x = - \frac{3}{2}

y = (x - 2 + 5) (x - 2 - 5)

x^{2} + 2 x + 3 y + 22 = 0

y = - \frac{1}{4} x^{2} + x + 3

y = - \frac{1}{4} x^{2} + x + 6

+ y = x^{2} - 6 x + 8